Question: An 8-foot by 10-foot floor is tiled with square tiles of size 1 foot by 1 foot. Each tile has a pattern consisting of four white quarter circles of radius 1/2 foot centered at each corner of the tile. The remaining portion of the tile is shaded. How many square feet of the floor are shaded?
[asy]
fill((5,5)--(5,-5)--(-5,-5)--(-5,5)--cycle,gray(0.7));
fill(Circle((-5,5),5),white);
fill(Circle((5,5),5),white);
fill(Circle((-5,-5),5),white);
fill(Circle((5,-5),5),white);
draw((-5,5)--(-5,-5)--(5,-5)--(5,5)--cycle);
[/asy]
Solution: The four white quarter circles in each tile have the same area as a whole circle of radius $1/2$, that is, $\pi(1/2)^2 = \pi/4$ square feet. So the area of the shaded portion of each tile is $ 1 - \pi/4$ square feet. Since there are $8\cdot 10 = 80$ tiles in the entire floor, the area of the total shaded region in square feet is \[
80\left(1 - \frac{\pi}{4}\right) = \boxed{80 - 20\pi}.
\]